Mathias Kvistgaarden and Ben Chrisene are set for some time on the sidelines after both picked up injuries in the 1-1 draw against Coventry City.
Both players were replaced in the second half of the fixture with Liam Manning now confirming the extent of their injuries.
"Ben's going to be eight weeks I think, he picked up a hamstring injury. We're always conscious about giving out time scales, it comes down to how the lad's body feels after the rehab," he said.
"It won't require surgery. It's very unfortunate, he had done terrifically well at Blackburn before going on international duty and now this, he had started to find the level."
With Jeffrey Schlupp also injured, Manning provided a further update on the left side of City's defence ahead of the weekend.
"(Schlupp)'s back on the grass, probably back in training next week. It's a little too soon for him. It's also a little too early for Lucien (Mahovo). As a group of staff, we're ready to take calculated risks but we don't want to be reckless. José (Córdoba) is back in, he was on the bike on Monday and then joined the squad. Shane (Duffy) picked up a calf injury and has been out for a little while."
For Kvistgaarden, Manning gave a timeframe of six weeks but also added the caveat that it would depend on the rehab process and how the Dane responded to it.
After scoring his first goal for the club against Coventry, it's a blow for the summer signing.
"Mathias is going to be six weeks roughly without being held to those timeframes. It was an innocuous landing. It doesn't require surgery which is good news but we'll see how he responds to the rehab," Manning added.
"It's hugely disappointing, his first goal as well, we'd seen a change in him in the last few weeks. He had settled and been sharper, clearer in what we needed him to do. It's going to happen in football, that's the importance of depth and competition. It's an opportunity for someone else to step up."
Reflecting on the weekend's result, Manning outlined transitions as the main area for the Canaries' struggles at the Coventry Building Society Arena.
Norwich took a first-half lead before absorbing a lot of pressure until stoppage time when Haji Wright would rescue a point for the hosts.
"The biggest issue was transition, keeping it. We gave it back too cheaply, we never got any control and ended up doing a huge amount of running defensively.
"It's the first time I've seen us like that, I'm sure it will happen again in the future but not very often. What it showed is that the group are willing to give everything, what do we look like on a bad day?"
On Saturday's opposition, the head coach spoke about their rise through the leagues and the job done by their coaching team to get them from non-league to the Championship.
Wrexham have just one win in their five Championship games to date with one draw and three defeats.
"The last few years have been exciting to watch, they've done an incredible job. Their recruitment, how they invested in the summer, they've signed a lot of players proven at the level.
"We have to look beyond the results and see that. We're at home and we'll need to take all the experiences from the opening game, dominate and make the game look how we want.
"They're well-organised and physical, hard to play against. We've done our work and know quite a few of their players as well. It's a tough game but one we'll be ready for."